Show that for a small value of the damping factor c/cc , the maximum amplitude of a forced vibration occurs when Wf= Wn and that the corresponding value of the magnification factor is ½ (c/c2).

Q: 3) A one-degree-of-freedom system has an effective mass M=4-kg, an effective spring stiffness…

A:

Q: 5. A weight of mass M = 8 kg is suspended by a spring with k = 10 N / m and c = 1.6 N s/m. The…

A: Given M=8kgK=10 N/mC=1.6 Ns/mThe governing equation of system isMx+Cx+kx=0˙¨

Q: ed from the deck with 4 flexible mounts. Determine combined spring constant of mounts such that the…

A:

Q: The beam shown in Fig. 4 is loaded with an air conditioning (AC) unit at its tip. The AC unit…

A: The question asks you to find the damping ratio and the maximum deflection of the beam when the…

Q: natural frequency of the system.

A: Given: A mass of 1 kg, m=1 kgAttached to two identical springs each of stiffness;  k=25 kN/mUnder…

Q: The 20kg block is subjected to the action of the harmonic force F=90cos6t N, where t is in seconds.…

A:

Q: A damped single-degree-of-freedom vibration system has m= 7 kg, c= 549 Ns/m, and k= 10 kN/m.…

A: In vibrating system, damping ratio represents the degree of dampness provided in the vibrating…

Q: A precision grinding machine is supported on an isolator that has a stiffness of 3 MN/m and a…

A:

Q: 2. Determine the equivalent damping of the system.

A: Given Data⇒

Q: A machine is represented as a single degree of freedom spring-mass-damper system. The machine has a…

A:

Q: An electric motor of mass 68 kg is mounted on an isolator block of mass 1200 kg and the natural…

A: Given 68 kg mounted on 1200kg m=1200+68=1268kg wn=160  rpm=160×2𝜋60=16.75rad/s F=1005m, w= 31.4…

Q: for the system shown determine the natural frequency and the damping factor

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Q: Replace the loading on the frame by a single resultant force. Take F₁ = 540 N. F = 220 N (Figure 1)…

A:

Q: 1. Consider the mass m in the connected system shown. The solid rod is assumed to have zero weight.…

A: Given:To find:Damping constant and natural frequency

Q: For a certain mass-spring system m = 100 kg and k = 8000 N/m. Determine the value of the critical…

A:

Q: Q1/ An instrument vibrate with a frequency of 1 Hz when there is no damping. When the damping is…

A: Answer: (a) The damping factor is 0.43588. (b) The logarithmic decrement is 3.04308.

Q: ] Derive the differential equation of motion for the system shown; Determine th e of the steady…

A: Given- m=6kg k=8 KN/m c=40 N-s/m Y=80mm=0.08m ω=30 rad/sec

Q: The phase angle describe the relative shift in the sinusoidal vibration of the spring mass system…

A: given; ϕ=phase anglex0=initial displacementx(t)=ω2x02+v02ω*sin(ωt+ϕ)and;ϕ=tan-1ωx0v0

Q: DETERMINE THE AMPLITUDE OF THE STEADY STATE VIBRATION AND ANGLE BY WHICH X LAGS Y.

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Q: 1. For the system shown, the spring constant k = 400 kN/m, damping coefficient zeta = 0.5 and the…

A:

Q: Determine the natural frequency

A: To find the natural frequency.

Q: An electrical switch gear is supported by a crane through a steel cable of length 4 m and diameter…

A: Given data: L=4 md=0.01 mT=0.01 s Need to determine the stiffness of the cable.

Q: .X2 kl ww W1= 6KN W2= 8000N W1 ▶X1 k2 ml kl 12 KN/cm W2 k2 2 = 15KN/cm

A:

Q: A machine is represented as a single degree of freedom spring-mass-damper system. The machine has a…

A: Find the damping factor as follows.

Q: 2- Weight W = mg k|2 V p = jacking force For the structure given above, assume that the weight of…

A: to findvelocity at t=1 sec when(a) undamped system(b) c=500 KN.sec/m

Q: A mass of flexible machine part, m1 of 10 ×1 kg was observed to vibrate badly at frequency of 10 Hz.…

A:

Q: for the system shown determine the natural frequency and the damping factor M1 a b M2 K M2 K

A:

Q: 1. Determine the equivalent damping of the system.

A: Given Data⇒

Q: A damped single-degree-of-freedom vibration system has m= 3.6 kg , c= 513 Ns/m , and k= 24 kN/m .…

A: m = 3.6 kg c = 513 Ns/m k = 24 kN/m = 24000 N/m

Q: b. A single degree of freedom suspension system is designed for a machine having a mass of 50 kg.…

A:

Q: Q2) ) A mass of 1 kg is to be supported on a spring having a stiffness of 9800 N/m. The damping…

A: Logarithmic decrement represents the rate at which the amplitude of free-damped vibrations reduces.…

Q: A vehicle of mass m = 500 kg travels over a long terrain that is approximately sinusoidal:y = d…

A: Given data as per questiona

Q: 1. For a single degree of freedom spring–mass–damper system with m = 1 kg, k = 4x104 N/m, and e = 10…

A: YOU ASKING ONLY PART C & D ,SO I PROVIDE ONLY THAT.

Q: The 45 kg piston is supported by a spring of modulus k = 35 kN/m. A dashpot of damping coefficient…

A: Write the given data. m=45 kgk=35 kN/mc=1250 Ns/mP=4000sin30tA=50×10-3 m2

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.